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2010 Infinite generation of the kernels of the Magnus and Burau representations
Thomas Church, Benson Farb
Algebr. Geom. Topol. 10(2): 837-851 (2010). DOI: 10.2140/agt.2010.10.837

Abstract

Consider the kernel Magg of the Magnus representation of the Torelli group and the kernel Burn of the Burau representation of the braid group. We prove that for g2 and for n6 the groups Magg and Burn have infinite rank first homology. As a consequence we conclude that neither group has any finite generating set. The method of proof in each case consists of producing a kind of “Johnson-type” homomorphism to an infinite rank abelian group, and proving the image has infinite rank. For the case of Burn, we do this with the assistance of a computer calculation.

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Thomas Church. Benson Farb. "Infinite generation of the kernels of the Magnus and Burau representations." Algebr. Geom. Topol. 10 (2) 837 - 851, 2010. https://doi.org/10.2140/agt.2010.10.837

Information

Received: 28 October 2009; Accepted: 15 January 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1201.20033
MathSciNet: MR2629766
Digital Object Identifier: 10.2140/agt.2010.10.837

Subjects:
Primary: 20F34, 20F36, 57M07

Rights: Copyright © 2010 Mathematical Sciences Publishers

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